Journal of Topology

Journal of Topology Advance Access originally published online on February 6, 2008
Journal of Topology 2008 1(2):342-361; doi:10.1112/jtopol/jtm013

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© 2008 London Mathematical Society

Dimension of asymptotic cones of Lie groups

Yves de Cornulier

IRMAR, Campus de Beaulieu, 35042 Rennes Cedex, France yves.decornulier@univ-rennes1.fr

We compute the covering dimension of the asymptotic cone of a connected Lie group. For simply connected solvable Lie groups, this is the codimension of the exponential radical.

As an application of the proof, we give a characterization of connected Lie groups that quasi-isometrically embed into a nonpositively curved metric space.

Received February 6, 2007.

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2000 Mathematics Subject Classification 22E15 (primary), 20F69, 22E25, 54F45 (secondary)

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This Article Abstract Full Text (PDF) Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Alert me to new issues of the journal Add to My Personal Archive Download to citation manager Request Permissions Google Scholar Articles by de Cornulier, Y. Social Bookmarking          What's this?